Is it obligatory to repeat the prayers that were performed without observing purification from madhy, and how should they be repeated?

The madhy (pre-seminal fluid) is impure and nullifies ablution. The male organ is purified by washing only the site of the impurity, and the garment is purified by sprinkling. Whoever prays with madhy on his body or garment, his prayer is invalid and must be repeated due to the absence of the condition of purity from filth. However, whoever prayed with madhy unknowingly of its presence, is not required to repeat past prayers, according to the more sound of the two scholarly opinions. And whoever is not certain that he has missed prayers, is not required to make them up.